Question: Express the radical using the imaginary unit, $i$. Express your answer in simplified form. $\pm\sqrt{-90}=\pm$
Solution: Background The imaginary unit ${i}$ is defined as $\sqrt{-1}$. So for any negative real number $-a$, we can express $\sqrt{-a}$ as ${i}\sqrt{a}$. Converting the Expression $\begin{aligned}\pm\sqrt{-90}&=\pm\sqrt{-1\cdot90} \\\\&=\pm\sqrt{-1}\cdot\sqrt{90} \\\\&=\pm{i}\cdot\sqrt{90} \\\\&=\pm3\sqrt{10}{i}\end{aligned}$ Summary $\pm\sqrt{-90}=\pm3\sqrt{10}{i}$